Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators

TL;DR

This paper introduces a class of quantum channels that are irreducibly covariant under a finite group generated by Weyl operators, generalizing quaternion groups, and explores their properties and examples.

Contribution

It defines and analyzes irreducibly covariant quantum channels related to Weyl group symmetries, including generalized Pauli channels and positive maps.

Findings

Characterization of irreducibly covariant quantum channels

Connection to generalized Pauli channels in non-Markovian dynamics

Examples of positive but not completely positive covariant maps

Abstract

We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly covariant quantum channels; that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.